My view is that the state can only deal with marriage as a civil institution. It should not get involved in the religious side. (Personally I have a strong feeling that there should be a complete split between religious and civil marriage)
In general I would agree with the first of the quoted sentences. The state has no business forcing churches to hold religious ceremonies. Any state interference in religion needs strong justification and I don't see it here.
I would disagree with the second since it seems to go too far (although this may be poor wording).
I don't know how things work in Maine but if I were talking about the UK I would say that registrars (who are civil servants) should be required to perform marriages - and should be subject to disciplinary action if they refuse. Any couple who are legally entitled to marry should be able to do so, regardless of the personal religious convictions of officials.
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